In a story today we analyze the relationship between the availability of firearms in the United States and suicide rates. Our main finding is that the suicide rate would likely decline significantly if guns weren’t used so widely by Americans to take their own lives. More specifically, we compare the number of Americans who commit suicide with firearms in the U.S. to four other rich Western countries — Australia, Canada, France, and the United Kingdom. While the Centers for Disease Control and Prevention reports that in the U.S. 50 percent of suicides are committed with guns, the OECD says that in these countries just nine percent are.

The difference forms the basis for an illustration of what the suicide rate would be in the U.S. if people killed themselves with guns as the same rate as people do in those four other countries. As noted in this story, this is purely a hypothetical: Nobody knows what would happen if firearm availability in the U.S. resembled levels of other developed countries. But three top experts on suicides and guns — Cathy Barber, who directs a suicide-reduction campaign at the Harvard School of Public Health, Daniel Webster, a professor at the Johns Hopkins Bloomberg School of Public Health, and Matthew Miller, a researcher at the Harvard School of Public Health – said this represented a valid methodology.

Our bottom line finding is that if the suicide by gun rate in the U.S. was similar to our group of four countries, the overall suicide rate would be between 20 and 38 percent lower than it is now. In other words, 8,534 to 16,334 fewer people would have died in 2014, the last year we have data.

To determine those figures, we went through a number of steps and made a number of assumptions. We began with the 42,773 people who commit suicide. According to CDC, 21,334 of them use guns, and 21,439 do not. If the U.S. mirrored the other Western countries, only 3,882 would use guns.

So in our model, those 3,882 remain as firearm deaths, leaving 17,452 who will not commit suicide using guns. Firearm suicide attempts succeed 90 percent of the time, so these 17,452 suicides correspond to 19,434 attempts that will not involve guns in our hypothetical. The question is what becomes of them.

Some of these people, without access to a gun, would likely just choose not to attempt to suicide at all. But it’s also very likely that some will choose a different method.

To be conservative in our calculation, we assumed that all of the people in this group do attempt to commit suicide using means other than firearms. The next question is how they do it.

This question is particularly important because different suicide methods have wide-ranging success rates. While 90 percent of people who attempt suicide with guns succeed, that’s only true of 81 percent of people who attempt to suffocate themselves, 32 percent of people who jump from a significant height, and 4 percent of people who attempt to poison themselves. (We’re using the CDC’s nonfatal self-harm data here, which includes the number of people who attempt self-harm that leads them to end up in the emergency room.)

It’s impossible to know what mix of these alternative methods people who no longer use guns would try. But we’ve come up with two estimates, which you can think of as the lower and upper bounds on the expected decline in suicide rates. Depending on which we use, we either find that the suicide rate declines 20 percent or 38 percent.

38 percent

In this estimate, we apply the same mix of methods that people currently use to attempt suicide – excluding firearms. This distribution – 51 percent poisoning, 24 percent cutting, four percent suffocation, one percent jumping and 20 percent other methods — has an overall fatality rate of 6 percent. In other words, 94 percent of the people who would otherwise have killed themselves with guns now would live.

Obviously, in this scenario, almost all the people who would have died with guns live. So, under this scenario, the total deaths from suicides would be 38 percent lower. Here’s how the math looks on that:

But this impact may be too high. Gun users could be more serious about dying than some people who cut themselves or take minor overdoses. That means, they may go to more extreme measures to make sure their suicide is successful. Someacademicresearchfinds that method choice is unrelated to the intensity of someone’s intent to die. That is, gun users are no more intent on dying than poison users, so there’s no reason to think they would attempt poisoning differently and die at a higher rate. However, somestudiesdraw the opposite conclusion.

20 percent

To consider a more conservative option, we apply the same mix of methods that people currently use who succeed at suicide – again, excluding firearms. Since this is replicating the mix of methods used by people who have a higher intent on killing themselves, it might reflect the gun suicide population better.

This distribution – 53 percent suffocation, 32 percent poisoning, five percent jumping, three percent cutting and seven percent other methods – has an overall fatality rate of 46 percent. In other words, just 54 percent of the people who would otherwise have killed themselves with guns now would live.

Under this scenario, the total deaths from suicides would be more modest 20 percent lower. Here’s how the math looks on that:

This latter estimate of the decline may be too low because it excludes people who are serious suicide attempters, but don’t die, skewing our distribution toward deadlier methods.

Reality may be somewhere in between these assumptions — in between those 20 and 38 percent figures.

And this range could be subject to other, unpredictable factors. There are, after all, many factors that go in to suicide rates that may change alongside a change in gun access. For instance, when less access to guns leads fewer people to die from suicide, rates may decline even further because of the copycat effect — that is, because fewer people are dying from suicide, fewer depressed people will be tempted to follow suit, so there will be fewer suicide attempters. On the other hand, it’s possible another highly lethal suicide method would emerge, like the use of pesticides in Southeast Asia.

But while the precise numbers may be hypotheticals, it seems clear that gun access has a clear link to suicide rates.